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We introduce the notion of amicable partitions for combinatorial manifolds with complementarity. We prove that any 4-dimensional combinatorial manifold X 4 9 satisfying complementarity has an amicable partition and any amicable partition determines X 4 9 up to isomorphism. This gives a short proof of the uniqueness of Kuhnel's 9-vertex complex projec- tive plane.

A short proof of the uniqueness of Kühnel's 9-vertex complex projective plane